scholarly journals Actions of the monodromy matrix elements onto $\mathfrak{g}\mathfrak{l}\left(m\vert n\right)$-invariant Bethe vectors

2020 ◽  
Vol 2020 (9) ◽  
pp. 093104
Author(s):  
A Hutsalyuk ◽  
A Liashyk ◽  
S Z Pakuliak ◽  
E Ragoucy ◽  
N A Slavnov
Keyword(s):  
Monodromy Matrix ◽  
Matrix Elements

COLORED EXTENSIONS OF GLq(2) QUANTUM GROUP AND RELATED NONCOMMUTATIVE PLANES

1995 ◽  
Vol 10 (19) ◽  
pp. 2851-2864 ◽  
Author(s):  
B. BASU-MALLICK
Keyword(s):  
Power Series ◽  
Quantum Group ◽  
Series Expansion ◽  
Braid Group ◽  
Group Representation ◽  
Monodromy Matrix ◽  
Power Series Expansion ◽  
Quadratic Algebra ◽  
Matrix Elements ◽  
Infinite Dimensional

An infinite-dimensional quantum group, containing the standard GLq(2) and GLp,q(2) cases as different subalgebras, is constructed by using a colored braid group representation. It turns out that all algebraic relations occurring in this “colored” quantum group can be expressed in the Heisenberg-Weyl form, for a nontrivial choice of corresponding basis elements. Moreover a novel quadratic algebra, defined through Kac-Moody-like generators, is obtained by making some power series expansion of related monodromy matrix elements. The structure of invariant noncommutative planes associated with this “colored” quantum group has also been investigated.

scholarly journals CONSTRUCTION OF MONODROMY MATRIX IN THE F-BASIS AND SCALAR PRODUCTS IN SPIN CHAINS

2001 ◽  
Vol 16 (12) ◽  
pp. 2175-2193 ◽  
Author(s):  
A. A. OVCHINNIKOV
Keyword(s):  
Scalar Product ◽  
Monodromy Matrix ◽  
Quantum Spin ◽  
Matrix Elements ◽  
Quantum Spin Chain ◽  
Usual Basis ◽  
The Matrix ◽  
General Scalar ◽  
Scalar Products

We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F-basis and the usual basis.

The light-scattering Mueller matrices for Rayleigh and Rayleigh-Gans-Debye approximation

1990 ◽  
Vol 55 (12) ◽  
pp. 2889-2897
Author(s):  
Jaroslav Holoubek
Keyword(s):  
Light Scattering ◽  
Theoretical Work ◽  
Matrix Elements ◽  
Elastic Light Scattering ◽  
Yield Information ◽  
Recent Theoretical Work ◽  
Particle Parameters ◽  
Complete Set ◽  
Single Matrix ◽  
Scattering Matrix Elements

Recent theoretical work has shown that the complete set of polarized elastic light-scattering studies should yield information about scatterer structure that has so far hardly been utilized. We present here calculations of angular dependences of light-scattering matrix elements for spheres near the Rayleigh and Rayleigh-Gans-Debye limits. The significance of single matrix elements is documented on examples that show how different matrix elements respond to changes in particle parameters. It appears that in the small-particle limit (Rg/λ < 0.1) we do not loose much information by ignoring "large particle" observables.

OPTICAL TRANSITIONS IN A PARABOLIC GaAs/Ga1-xAlxAs SUPERLATTICES

2001 ◽  
Vol 08 (03n04) ◽  
pp. 321-325
Author(s):  
ŞAKIR ERKOÇ ◽  
HATICE KÖKTEN
Keyword(s):  
Transition Matrix ◽  
Optical Transition ◽  
Matrix Elements ◽  
Electron States ◽  
Parabolic Potential ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Transition Matrix Elements ◽  
Scf Calculations

We have performed self-consistent field (SCF) calculations of the electronic structure of GaAs/Ga 1-x Al x As superlattices with parabolic potential profile within the effective mass theory. We have calculated the optical transition matrix elements involving transitions from the hole states to the electron states, and we have also computed the oscillator strength matrix elements for the transitions among the electron states.

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